# Precalculus - Sinusoids



## Sandstone-Shadow (Feb 16, 2009)

Is anyone here currently taking precalc/has taken precalc that understands sinusoids? I'm really not understanding them, particularly with writing equations from word problems. And what exactly are the phase shift and vertical translation? Those are confusing me too. Can anyone help?


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## Tailsy (Feb 16, 2009)

I dunno what those are, but In America they seem to like using confusing names for things... do you have an example? I miiight be able to help (but I'm maths-retarded so).


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## Sandstone-Shadow (Feb 16, 2009)

Well, this is one of the questions...


> A ferris wheel 50 feet in diameter makes one revolution every 40 seconds. If the center of the wheel is 30 feet above the ground, how long after reaching the low point is a rider 50 feet above the ground?


And the equation is supposed to be written in the form y=a sin(b(x-h)) + k or y=a cos(b(x-h)) + k.

How would you write the equation for that problem?


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## Tarvos (Feb 16, 2009)

Draw the ferris wheel. Some of these numbers mean amplitude,frequency, and displacement. I'm gonna leave it up to you to figure out which is which because else I'm handing you the question on a silver platter, which I definitely can do, but won't. 

It's important with a sinusoid function that you realise that the rotation of the ferris wheel is a periodical function: basically, every x amount of time you have the same sine graph. Basically, you are expressing the point a rider is at as a function of time. So, after t seconds a rider will be at position x. Because it's periodical, it will always be within a certain range. If you read the question carefully, you can determine what the max and min height is the rider can reach. You also know the stable equilibrium point. The amount of time the ferris wheel needs to make one revolution (i.e. the time it takes for the sine graph to repeat itself) is also known. You can work from there, figure out what the equation is supposed to be (use the right dimensions!) and once you know the equation, you can fill in the numbers and do the arithmetic.


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## Sandstone-Shadow (Feb 18, 2009)

Ah, okay, that helps. ^^ We went over a bunch of problems in class, and that really helped, too. =D Thanks!


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